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## PowerPoint Slideshow about 'Tevatron Collider Monte Carlo' - wendi

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Outline

- What’s going on here?
- Random numbers
- Assumptions
- Collider parameters
- Randomizations
- How does this work?
- What can we learn from this model?
- Web Interface, “beta” version

E. McCrory

What’s going on here?

- Phenomenological (non-analytic) model of the Tevatron Collider Complex
- Began during Run I, with Vinod, GPJ & others helping
- McGinnis’s ordered me to revive it now.
- Incorporate randomness
- Downtime
- For the Tevatron, stacking and the PBar Source
- Variations in all realistic parameters
- E.g., transmissions during a shot, lifetimes, uncertainty in exactly how many pbars we extract, shot setup time, downtime, etc….
- Develop intuition for controlling stores
- Based on these assumptions and randomizations
- Many already have this intuition, but not all….

E. McCrory

Current Features

- Represents Run II performance, today.
- Easy to change to reflect “tomorrow’s” performance
- Many algorithms for ending stores
- Linux, C++
- Pretty good random number generator: drand48()
- Can simulate 10,000 weeks in about 23 seconds
- Command-line arguments: scan a parameter
- Easily adaptable, through recompilation

E. McCrory

Limitations

- This is a phenomenological model!
- L (t=0) = K Np(0) Npbar(0) / (εp(0) + εpbar(0))
- K = (1.331 ± 10%)βγ / β*[cm]
- Downtime over 24 hours is not considered.
- Extended shutdowns are irrelevant.
- Performance in the model does not improve.
- Just random fluctuations around specified performance.

E. McCrory

Unix’s drand48( ); class RandomLinear

RandomLinear(2.0, 12.0)

RandomLinear(0.0, 5.0)

Random NumbersE. McCrory

(Not shown): class RandomBooleanClass RandomLikely

Product of these two distributions

(0, 5, 2) and (-2, 12, 8)

E. McCrory

Stacking rate:

12 (1-S/300) [mA/hr]

Stacking off:

-0.001 S [mA/hr]

Luminosity Lifetime

L (t) = L (0)e-t/τ(t)

τ(t) = τ(0) + C1 t C2

C1= 1.8 ± 0.2

C2 = 0.595 ± 0.005

Collider Parameter AssumptionsE. McCrory

Randomization Assumptions (PBar & Shot)

E. McCrory

How does this work?

- Step size = 0.1 hours
- Diminish the luminosity
- Stack
- See if anything has failed
- Stacking stops
- For a RandomLikely down time
- Stacking slows down
- For this step, by up to 50% (RandomLinear)
- Lose a store
- Plus a RandomLikely recovery time.
- Lose a stack
- Plus a RandomLikely recovery time.
- If stack or store is lost, will stack to a reasonable stack size and shoot
- Reasonable = 100 mA
- If a stack is lost, we keep the store in for a long time!
- Otherwise, when we reach the “Target Stack Size” we start shot setup.
- Shot setup time varies from 1.2 to 4 hours
- Repeat for N weeks, dumping all sorts of relevant data.

E. McCrory

Well-measuredInitial Luminosity Lifetime Assumption

Initial Luminosity Lifetime, Hours

The rest is an educated guess

Initial Luminosity, E30 cm-2 sec-1

E. McCrory

Lifetime: Real vs. Sim

Luminosity, E30

Six typical, simulated stores

Two recent, real stores

Hours into the store

E. McCrory

Shot Setup Duration, Real vs. Sim

RandomLikely(1.2, 4.0, 2.2)

Data from the Supertable

Setup Duration, Hours

E. McCrory

What Can We Learn from this Model?

- Replicating typical performance, today
- Typical store data, typical weeks.
- How should we end stores?
- When we have a choice.
- Tevatron up-time
- Where do we integrate luminosity?
- The impact of future improvements

E. McCrory

Typical 2-week period, Stacking to 170 mA

Stack Size (mA)

Stacking downtime

Dropped stacks

Lost stores

Luminosity (E30)

Day number

E. McCrory

Typical Store Data

E. McCrory

Typical Weeks

E. McCrory

Algorithms for Ending a Store

- When one of these crosses the target:
- Stack Size
- Store Duration
- Integrated luminosity of the store
- Instantaneous luminosity falls too low.
- When 2 or more of these are satisfied
- Compare “Expected Luminosity” vs. luminosity now
- Ratio
- Difference
- “Figure of Merit”
- No good …

E. McCrory

Explore the Search for the Best Target Stack Size

- Tevatron up time varies over several runs
- 94% per hour to 99% per hour
- E.g., the probability a store lasts 20 hours is:
- (0.94)20 = 0.290
- (0.96)20 = 0.442
- (0.99)20 = 0.818
- Charts and tables …
- Optimization, downtime, Run Coordinator tables and charts, etc.

E. McCrory

We can benefit from trying to go to larger stacksRun eight simulations of a 5000-week period, each with a different value for the Target Stack Size

σ≈ 25%, 1500 nb-1

Average Weekly Integrated Luminosity, 1/nb

Target Stack Size, mA

E. McCrory

Where do we Integrate Luminosity?

Fraction Integrated per bin

Fraction Integrated per bin

Target Stack Size = 180 mA

E. McCrory

Instantaneous Luminosity, E30 cm-2 sec-1

Tevatron Up fraction:

0.94 per hour

20 Hours: 0.290

0.95

0.96

0.97

0.98

0.99

0.818

Run for 5000 Weeks, using “Target Stack Size”Tev Up Fraction: 0.99

Up: 0.98

Up: 0.97

Average Weekly Integrated Luminosity, 1/nb

Up: 0.96

Up: 0.95

Up: 0.94

Target Stack Size, mA

E. McCrory

Recovery time after lost store: RandomLikely(1, 24, 10)Tevatron up-time per week vs. Target Stack Size

0.99

0.98

0.97

Hours of store per week

0.96

0.95

0.94

E. McCrory

Target Stack Size

Fraction of Stores Lost vs. Target Stack Size

0.94

0.95

0.96

0.96

0.97

0.98

Fraction of stores lost

We have been losing ~55% of stores

0.99

This may be the best way to

set the UpTime parameter

E. McCrory

Target Stack Size

More Esoteric Stuff

- Different end-of-store algorithms
- “Luminosity Potential”
- Startup after a dropped store
- “Reasonable Stack” vs. Target Stack
- “Reasonable Stack” in the context of “Luminosity Potential”
- Better stacking

E. McCrory

Luminosity Difference or Ratio Algorithm

- Use chart, here.
- Two different ways to end stores:
- When the ratio between the expected luminosity and the current luminosity exceed some constant, V.
- When the difference exceeds constant, L.
- * Generated by the model; error bars (σ) ≈ 20%

Expected

Luminosity*

Initial Luminosity, E30

Recent stores

Stack Size, mA

E. McCrory

Using Algorithm to End Stores on the Luminosity Difference

0.99

Average Luminosity per Week, 1/nb

0.98

0.97

0.96

0.95

0.94

Value of the constant L: Expected Luminosity Difference

E. McCrory

Using Algorithm to End Stores on the Luminosity Ratio

0.99

0.98

Average Luminosity per Week, 1/nb

0.97

0.96

End store when:

Expected Lum ≈ 5 L (now)

0.95

0.94

Value of the constant V: Expected Luminosity Ratio

E. McCrory

Reasonable Startup Stack Size?

Startup Stack Size:

40, 60, 80, 100, 120, 140, 160

Average Weekly Integrated Luminosity, 1/nb

Tevatron Uptime: 0.96

∴ Waiting for a good stack after a lost store: +3%

Target Stack Size, mA

E. McCrory

Startup Stack Size and Luminosity Potential (Ratio)

Startup Stack Size:

40, 60, 80, 100, 120, 140, 160

Average Weekly Integrated Luminosity, 1/nb

Tevatron Uptime: 0.96

Lum(Stack now) ≈ 4*(Lum now);

Startup Stack Size: Can get ~6%.

Luminosity Potential ratio

E. McCrory

Zero Stack Stacking rate: 18 mA/hr

0.99

0.98

0.97

0.96

Average Weekly Integrated Luminosity, 1/nb

0.95

0.94

Target Stack Size, mA

E. McCrory

Compare Different Stacking Rates

S=0 rate: 18 mA/hr

+26%

+13%

Average Weekly Integrated Luminosity, 1/nb

12 mA/hr

Tevatron Up: 0.96

Target Stack Size, mA

E. McCrory

Web Interface

- http://mccrory.fnal.gov/testForm.html
- Will do one run of N weeks with one set of parameters.
- Probably not fully debugged, yet.

E. McCrory

What’s Next?

- Use Valary Lebedev’s analytical model of the luminosity
- To represent more accurately the luminosity lifetime of very large stores.
- Internal improvements
- Exactly match all real numbers
- Especially in the transmission of PBars to low beta.
- Incorporate Recycler
- Study various operational transfer scenarios

E. McCrory

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